How to Detect Possible Additional Outliers

Case of Interval Uncertainty

authored by: Hani Dbouk, Steffen Schön, Ingo Neumann, Vladik Kreinovichy
Abstract: In many practical situations, measurements are characterized by interval uncertainty - namely, based on each measurement result, the only information that we have about the actual value of the measured quantity is that this value belongs to some interval. If several such intervals - corresponding to measuring the same quantity - have an empty intersection, this means that at least one of the corresponding measurement results is an outlier, caused by a malfunction of the measuring instrument. From the purely mathematical viewpoint, if the intersection is non-empty, there is no reason to be suspicious. However, from the practical viewpoint, if the intersection is too narrow - i.e., almost empty - then we should also be suspicious, and mark this as an possible additional outlier case. In this paper, we describe a natural way to formalize this idea, and an algorithm for detecting such additional possible outliers.
Organisation(s): Institute of Geodesy
External Organisation(s): University of Texas at El Paso
Type: Article
Journal: Reliable Computing
Volume: 28
Pages: 100-106
No. of pages: 7
ISSN: 1385-3139
Publication date: 06.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Computational Mathematics, Applied Mathematics
Electronic version(s): https://www.cs.utep.edu/vladik/2020/tr20-67b.pdf (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{7506ca8889fd4c7b8882bc94e6e3890b,
title = "How to Detect Possible Additional Outliers: Case of Interval Uncertainty",
abstract = "In many practical situations, measurements are characterized by interval uncertainty - namely, based on each measurement result, the only information that we have about the actual value of the measured quantity is that this value belongs to some interval. If several such intervals - corresponding to measuring the same quantity - have an empty intersection, this means that at least one of the corresponding measurement results is an outlier, caused by a malfunction of the measuring instrument. From the purely mathematical viewpoint, if the intersection is non-empty, there is no reason to be suspicious. However, from the practical viewpoint, if the intersection is too narrow - i.e., almost empty - then we should also be suspicious, and mark this as an possible additional outlier case. In this paper, we describe a natural way to formalize this idea, and an algorithm for detecting such additional possible outliers.",
keywords = "interval uncertainty, outliers, probabilistic approach",
author = "Hani Dbouk and Steffen Sch{\"o}n and Ingo Neumann and Vladik Kreinovichy",
note = "Funding information: This work was supported by the German Research Foundation (DFG) as a part of the Research Training Group i.c.sens (grant GRK2159) and by the Institute of Geodesy of the Leibniz University of Hannover. It was also supported in part by the US National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science) and HRD-1242122 (Cyber-ShARE Center of Excellence). This paper was written when V. Kreinovich was visiting Leibniz University of Hannover. The authors are grateful to the anonymous referees for valuable suggestions.",
year = "2021",
month = jun,
language = "English",
volume = "28",
pages = "100--106",
journal = "Reliable Computing",
issn = "1385-3139",
publisher = "Springer Netherlands",
}